Medical contrast agents as promising tools for biomacromolecular SAXS experiments

Lanthanide-based complexes are presented as a promising class of molecules for efficient SAXS contrast-variation experiments. Their interactions and contrast properties are analyzed for an oligomeric protein and a protein–RNA complex.

Crystals of P1 were obtained by the hanging drop technique by mixing one volume of 12 mg/mL protein solution in aqueous buffer (20 mM Tris pH 7.5 and 150 mM NaCl) and one volume of well solution consisting in 100 mM tri-sodium citrate pH 5.6, 200 mM sodium potassium tartrate, 1.9 to 2.4 M ammonium sulphate. Prior to data collection, the sample was cryo-cooled in liquid nitrogen using a cryo-solution consisting in the crystallization condition supplemented with 25% glycerol.
Diffraction data were collected at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) on FIP-BM30A beamline. Diffraction frames were integrated using the program XDS (Kabsch, 2010), and the integrated intensities were scaled and merged with the programs SCALA and TRUNCATE from the CCP4 program suite (Winn et al., 2011). The structure was determined by molecular replacement using PHASER using as search model the PDB file 1G2I. Refinement was performed with PHENIX (Afonine et al., 2012). The model was successively optimized through iterative cycles of refinement and model building in COOT (Emsley et al., 2010). Data and refinement statistics are summarized in Table S4. The atomic coordinates and measured structure factor amplitudes have been deposited in the Protein Data Bank with accession code 7QO8.

S3. SAXS theory, experiments and data reduction
For isotropically oriented and non-interacting particles in solution, the scattered intensity I(q) can be written as (Lindner & Zemb, 2002): is the modulus of the scattering vector, λ the X-ray wavelength, and 2θ the scattering angle. The brackets indicate an average over all orientations of the solubilized particles. ρ and ρsol are the electron densities of the particles and of the bulk solvent, respectively. Importantly, the integral runs over the entire volume of each particle, including areas where the solubilized particle (protein, macromolecular assembly) induces a different electron density than the one of the unperturbed bulk solvent. In particular, it can include a hydration shell in the vicinity of the particle surface (Svergun et al., 1998).
All SAXS experiments were carried out in flow mode on the SWING beamline (https://www.synchrotron-soleil.fr/en/beamlines/swing) at SOLEIL synchrotron (Saint Aubin, France), using an X-ray energy of 12.00 or 14.00 keV and a sample-detector distance of 1.79 or 2.00 m. For each sample a volume of 40 μL was circulated at 75 μL/min through a thermalized Quartz capillary of 1.5 mm diameter and 10 μm wall thickness, inserted within a vacuum chamber (David & Perez, 2009).
Series (typically 5 to 30) of individual 0.5 or 1 s time frames were collected at 15 ⁰C on an Aviex CCD Buffer intensities were subtracted from sample intensities using PRIMUS (Franke et al., 2017), after careful calibration against the logarithm of the measured transmissions (which depends linearly on the concentrations, Fig. S6 A-C), following a previously established protocol (Gabel, Engilberge, Pérez, et al., 2019). This protocol aims at minimizing mismatches between the background levels of buffers and samples which can occur in practice due to slight concentration differences of strongly scattering contrast agents in the molar concentration range used here. While the buffer signals do not evolve linearly over the entire concentration-and q-range (see, e.g., Fig. S7), we found that an approximation of a local linear interpolation, based on the most adjacent concentrations, yielded very satisfactory matches between sample and buffer levels over the whole q-range after calibration ( Fig. S6, S7, S8).
The stability and limits of this approach are illustrated in Figure S11, which shows that the linear interpolation requires a sufficiently dense series of experimental contrast points. Typically, the spread between adjacent concentrations should not exceed about 20% of the maximum concentration, i.e. a minimum of 5-6 equally spaced data points should be available. Figure S12 shows the entire q-ranges of the resulting subtracted data sets up to lowest and highest values measured. The low (and mostly constant) noise level at high q-values illustrates that buffer background levels match the sample background levels in general well, even though occasionally a slight over-subtraction is observed (detectable by zones of missing data points in the logarithmic plots). At very low angles, a slight mismatch of parasitic scattering was observed in some cases and the respective data points were discarded for the analysis in Figures 1-3 (as were data at high angles that contributed essentially noise).
In the case of the protein and protein-RNA complex, the respective volume fractions (v/v %) were very small (< 0.5% in all cases) and thus not taken into account in the subtraction process. The SAXS curves of the free contrast agents (i.e. in the absence of bio-macromolecules) were obtained by subtracting the respective 0 mM reference buffers from the Gd-HPDO3A and iohexol solutions at various concentrations ( Fig. S7 and S8). A weighted subtraction, taking the high (up to 40-50%) volume fractions of contrast molecules into account, did not change the shapes of the subtracted curves and the fitted parameters significantly, as illustrated for Gd-HPDO3A (Fig. S13). This is due to the fact that the background levels of aqueous buffers are much lower than those of buffers containing contrast molecules, and are essentially flat in the q-ranges of interest.

S4. SAXS data analysis
Basic parameters (forward scattered intensity I(0), radii of gyration RG, maximum dimensions Dmax and pair distance distribution functions p(r)) were extracted from the final 1D curves by using the Guinier approximation (Guinier, 1939) with the programs PRIMUS and GNOM from the ATSAS package (Franke et al., 2017) (Table S3). The experimental contrast match points (CMPs, i.e. I(0)=0) of P1 and aIF2-tRNA in Gd-HPDO3A were determined by plotting the square root of the forward scattered intensity, √I(0), vs contrast agent concentration (in mM) and applying a linear fit (Jacrot, 1976).  (Voss & Gerstein, 2005, Kharakoz, 1997, Creighton, 1993, Jacrot, 1976. Solvent-excluded volumes and electron densities of iohexol and Gd-HPDO3A were determined from their measured volumes (Table S2) and chemical formulae. All parameters are reported in Table S1.
The slope at the origin of the √I(0) P1 iohexol data (i.e. the relative decrease of √I (0) (Table S1). The ratio √I(0)P1, 92 mM / √I(0)P1, 0 mM was determined from the respective I(0) values determined by the Guinier fits (Table S3) and was 0.933. Note that Eq. S2 neglects potential changes of the overall hydration shell density of P1 in the range between 0 and 92 mM iohexol.
The experimentally determined CMP of P1 in iohexol (Fig. 3A, inset) was determined as 0.411 e -/Å 3 and inferior to the range of values calculated from the protein sequence (Table S1). In order to explain this discrepancy, we postulate a negative average hydration shell contrast Δρhydr at higher iohexol concentrations, while N iohexol molecules can be bound in parallel to P1 (Eq. S2). The condition √I (0) = 0 at the CMP yields the following equation: The strong inter-particle interactions between free Gd-HPDO3A molecules (which carry no net charge) were analyzed by a modified hard-sphere interaction potential (Fournet, 1951): C is a factor that depends on sample concentration and the number of electrons per particle, v0 = (4/3)·π·R 3 is the volume of a spherical particle with radius R, and v1 the average volume available for each particle in solution. Φ(qa) is the form factor of a sphere of radius a: In the case of a strict hard-sphere inter-action potential, d has a constant value of 2R and a = R. However, we did not obtain satisfactory fits when assuming that Gd-HPDO3A particles can contact each other directly (Fig. S5). Rather, it was necessary to introduce a value d > 2R which allowed to fit Gd-HPDO3A curves at all concentrations in a very satisfactory manner (Fig. 6).
Fits of all atomic models (P1, aIF2-tRNA, iohexol) against experimental SAXS curves were carried out with CRYSOL (version 2.8.2), imposing the bulk solvent electron density as a fixed value, calculated as described above from the values reported in Table S2, applying appropriate dilution factors. Default values of all available parameters (number of harmonics, Fibonacci grid, and maximum q) were used, and an optimization by a constant background subtraction was deactivated. Thus, in general, the only free fit parameter of the CRYSOL fits was the hydration shell.
An exception to this procedure are the results shown in Fig. S3: here, the density of the hydration shell was imposed as fixed in each case (screening a range from -0.03 to +0.03 e -/Å 3 ) to calculate a theoretical curve and no fit against experimental SAXS data was carried out. The value of the imposed hydration shell density yielding the best agreement between the radius of gyration of the resulting theoretical curve with the respective experimental SAXS curve was identified, and then compared to the value of fits with a variable hydration shell density, as described above.  S1 P1, aIF2, tRNA, iohexol and Gd-HPDO3A volumes, molecular masses, partial

specific volumes and electron densities
The values for proteins and the RNA were calculated from the sequences (Fig. S9) and residue and nucleotide volume ranges reported in literature (Voss & Gerstein, 2005, Kharakoz, 1997, Creighton, 1993, Jacrot, 1976. The values for iohexol and Gd-HPDO3A were calculated from their chemical formula and solvent-excluded volumes determined from the respective stock solutions (Table S2).
c Maximum q-range were data point were available. Final datasets are more restricted due to the elimination of parasitic scattering at very low angles and due to noise at high angles. d RG is actually a complex number since RG 2 is negative.

Additional SI material
The SAXS curves and the CRYSOL fit of the atomic macromolecular structures from Figures 1 to 3 have been deposited in the SASBDB databank (Kikhney et al., 2020) and can be accessed and downloaded using the following links:    sample and the respective aligned buffers at about 500, 1000 and 1500 mM when using an interpolation based on only half the data points (nearest neighbors about ± 500 mM).

Figure S12
Full ranges of SAXS data recorded on P1 and aIF2-tRNA in Gd-HPDO3A and P1 in iohexol. This figure presents the data and fits shown in Figure 1-3 B as opaque, supplemented by the data points (shown in semi-transparent mode) at very low angles and at high angles that were discarded and not used for the data analysis, due to artifacts (buffer mismatch, parasitic scattering at low angles etc). All data points with negative intensities (mainly at high angles due to buffer oversubtraction) are not included.

Figure S13
Impact of buffer subtraction taking volume fraction into account. This figure compares isolated Gd-HPDO3A data, subtracted with the 0 mM buffer without taking the volume fraction v/v occupied by the contrast molecules into account (opaque points, identical to the data shown in Fig. 6).
The transparent points show the subtracted curves with a weighted 0 mM buffer subtraction, diminished by the volume fraction that the contrast molecules occupy (calculated from Table S2). The inset table shows the fit parameters with this weighted SAXS curves. The fit values shown here are very similar to the ones in Figure 6, obtained for the non-weighted buffer subtraction, typically within 1% (with an exception of the data at 1341 mM).